THE THEORY DCF<sub>p</sub>A EXISTS FOR<i> p</i> &gt; 0

We prove that the elementary class of differential-difference fields in characteristic <i>p</i> &gt; 0 admits a model companion. In the terminology of Chatzidakis–Pillay [4], this establishes that the class of differentially closed fields of characteristic p, equipped with a generic differential automorphism, is elementary; that is, DCF<sub>p</sub>A exists. Along the way, we also provide alternative first-order axiomatisations for DCF (differentially closed fields) and for DCF<sub>0</sub>A.

Publication Details

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Research Explorer (The University of Manchester)
Published
2025-10-02
Primary Topic
Homotopy and Cohomology in Algebraic Topology
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article
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THE THEORY DCFpA EXISTS FOR p > 0

Research Explorer (The University of Manchester)
Homotopy and Cohomology in Algebraic Topology
article

THE THEORY DCFpA EXISTS FOR p > 0

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Abstract

We prove that the elementary class of differential-difference fields in characteristic <i>p</i> &gt; 0 admits a model companion. In the terminology of Chatzidakis–Pillay [4], this establishes that the class of differentially closed fields of characteristic p, equipped with a generic differential automorphism, is elementary; that is, DCF<sub>p</sub>A exists. Along the way, we also provide alternative first-order axiomatisations for DCF (differentially closed fields) and for DCF<sub>0</sub>A.

Research Explorer (The University of Manchester)
Openalex Percentile: Top 26%
Homotopy and Cohomology in Algebraic Topology
Open Access PDFOpenAlex
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THE THEORY DCF<sub>p</sub>A EXISTS FOR<i> p</i> &gt; 0 · Research Explorer (The University of Manchester) (2025) | TGRS Research Map | TGRS